Question

Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.
a. How long is the belt?
b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground.
c. We need a ramp to the window. How long would it need to be?

Answer 1

Draw some diagrams first to help visualize (if you need to)

a.
so one leg is 100ft and the other is 150ft
use Pythagorean theorem
for legs a and b and hytponuse length c
a²+b²=c²
so
given legs 100 and 150
100²+150²=c²
10000+22500=c²
32500=c²
sqrt both sides
50√13=c
the belt is 50√13 ft

b.
so, we take the point of the lower end of the belt and connect it to the window with a line
the base of the belt is 100ft ffrom the silo
since it is 45 degerees, and the base is 100ft, the height is 100ft as well
the height of the window from the ground is 100ft

c. ok, use special right triangles 
45-45-90 triangle
if one leg is x then the hypontuse is x√2
so one leg is 100ft so the hytponuse is 100√2 ft
the ramp must be 100√2 ft





a. 50√13 ft
b. 100 ft
c. 100√2 ft